Indiana University leases WATS lines and is chargedaccording to the following rules: $400 per month for eachof the first five lines; $300 per month for each of the nextfive lines; $100 per month for each additional line. TheCollege of Arts and Sciences makes 150 calls per hour, theSchool of Business makes 120 calls per hour, and the rest of the university makes 30 calls per hour. Assume that eachline can handle 30 calls per hour. Thus, the university willrent 10 WATS lines. The university wants to determine howmuch each part of the university should pay for long-distancephone service.a Set up a characteristic function representation of theproblem.b Use the Shapley value to allocate the university’slong-distance phone costs.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Indiana University leases WATS lines and is charged
according to the following rules: $400 per month for each
of the first five lines; $300 per month for each of the next
five lines; $100 per month for each additional line. The
College of Arts and Sciences makes 150 calls per hour, the
School of Business makes 120 calls per hour, and the rest
of the university makes 30 calls per hour. Assume that each
line can handle 30 calls per hour. Thus, the university will
rent 10 WATS lines. The university wants to determine how
much each part of the university should pay for long-distance
phone service.
a Set up a characteristic function representation of the
problem.
b Use the Shapley value to allocate the university’s
long-distance phone costs.
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